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Unformatted text preview: 18.02a Practice Midterm Questions, Fall 2009 Problems 1-5 cover material from the first unit. This will be on the midterm, but wont be emphasized. Problems 1-5 take about 1-1.5 hours, problems 6-17 take 2-3 hours. The actual test will be shorter designed to take 2 hours, with simpler arithmetic. Problem 1. Consider the point P = (20 , , 0), the plane P : x + 2 y + 3 z = 6 , and the point Q = (1 , 1 , 1) on P . a) Compute the distance from P to P . b) Give parametric equations for the line through P and perpendicular to P . c) Find the point of intersection between P and the line of part(b). For later reference, call this point R. d) Find the angle, PQR. e) By computing | PR | directly, verify your answer to part (a). f) Find the area of the triangle with vertices P, Q and R. Problem 2. Suppose tape is unwound from a roll in such a way that it is always vertical. Assuming the roll is centered at the origin and has radius 2, and the end of the tape starts at the point (2 , 0), give parametric equations for the path traced out by the end of the roll. For what values of your parameter does this make sense? Problem 3. The motion of a point P is given parametrically by-- OP = r ( t ) = h 4sin t, 5cos t, 3sin t i ....
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